Find the transformed equation of $x \cos \theta+y \sin \theta=p$, when the axes are rotated through an angle $\theta$.

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Aicharya · Accepted Answer

Given $x \cos \theta+y \sin \theta=P$ ...(i) The axis are rotated through angle $(\theta)$, then $\begin{array}{c|c|c} & x & y \ x & \cos \theta & -\sin \theta \ \hline y & \sin \theta & \cos \theta \end{array}$ $\Rightarrow \quad x=X \cos \theta-Y \sin \theta \text { and } y=X \sin \theta+Y \cos \theta$ Put in Eq. (i) $\begin{aligned} & \Rightarrow X \cos ^2 \theta-Y \sin \theta \cdot \cos \theta+X \sin ^2 \theta+Y \sin \theta \cdot \cos \theta=P \ & \Rightarrow X=P \end{aligned}$

Find the transformed equation of \(x \cos \theta+y \sin \theta=p\), when the axes are rotated through an…

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